Chapter 6
6.1 a Relative frequency approach
6.2 a Subjective approach
6.3 a {a is correct, b is correct, c is correct, d is correct, e is correct}
6.4 a Subjective approach
b The Dow Jones Industrial Index will increase on 60% of the days if economic conditions remain
6.6 {Adams wins. Brown wins, Collins wins, Dalton wins}
6.7a P(Adams loses) = P(Brown wins) + P(Collins wins) + P(Dalton wins) = .09 + .27 + .22 = .58
6.8 a {0, 1, 2, 3, 4, 5}
b {4, 5}
6.9 {Contractor 1 wins, Contractor 2 wins, Contractor 3 wins}
6.11 a {Shopper pays cash, shopper pays by credit card, shopper pays by debit card}
b P(Shopper pays cash) = .30, P(Shopper pays by credit card) = .60, P(Shopper pays by debit card)
= .10
6.13 {single, divorced, widowed}
6.15 a P(single) = .15
b P(adult is not divorced) = P(single) + P(married) + P(widowed) = .15+ .50 + .10 = .75
c P(adult is either widowed or divorced) = P(divorced) + P(widowed) = .25 + .10 = .35
6.18 a
57.
7.
4.
)B(P
)BandA(P
)B|A(P
1
11
11 ===
b
43.
7.
3.
)B(P
)BandA(P
)B|A(P
1
12
12 ===
2
B
1
A
6.20 The events are not independent because
.
6.21 a P(
1
A
or
1
B
) =
)BandA(P)B(P)A(P
1111
−+
= .6 + .7 – .4 = .9
b P(
1
A
or
2
B
) =
)BandA(P)B(P)A(P 2121 −+
= .6 + .3 – .2 = .7
1
A
6.24 P(
1
A
) = .15 + .25 = .40, P(
2
A
) = .20 + .25 = .45, P(
3
A
) = .10 + .05 = .15.
P(
1
B
) = .15 + 20 + .10 = .45, P(
2
B
) = .25 + .25 + .05 = .55.
6.25 a P(
2
A
|
2
B
) =
2
B
556.
45.
25.
)A(P
)BandA(P
22 ==
1
B
1
A
1
A
2
A
2
B
2
B
2
B
3
A
1
B
3
A
1
B
3
A
1
B
455.
55.
25.
)B(P
)BandA(P
22 ==
6.27 a P(promoted | female) =
20.
12.03.
03.
)female(P
)femaleandomotedpr(P =
+
=
c No, because promotion and gender are independent events.
6.28 a P(debit card) = .04 + .18 + .14 = .36
6.29 a P(Less than high school) = .057 + .104 = .161
b P(college/university | female) =
6.30 a P(He is a smoker) = .12 + .19 = .31
b P(He does not have lung disease) = .19 + .66 = .85
c P(He has lung disease | he is a smoker) =
6.31 The events are dependent because P(he has lung disease) = .15, P(he has lung disease | he is a
smoker) = .387
6.32a. P(manual | math-stats) =
390.
36.23.
23.
)statsmath(P
)statsmathandmanual(P =
+
=
−
−
6.33 a P(customer will return and good rating) =.35
6.34 a P(ulcer) = .01 + .03 + .03 + .04 = .11
6.35 a P(Insufficient work | 25-54) =
252.
214.180.320.
180.
)5425(P
)5425andworkntInsufficie(P =
++
=
−
−
b P(65 and over) = .029 + .011 + .016 = .056
6.37 a P(above average | murderer) =
563.
48.
27.
21.27.
27.
)murderer(P
)murdererandaverageabove(P ==
+
=
b No, because P(above average) = .27 + .24 = .51, which is not equal to P(above average
testosterone | murderer).
6.40a
636.
250.
159.
091.159.
159.
)300thanlessEnrollment(P
)300thanlessenrollmentandcrimeViolent(P ==
+
=
b.
205.
777.
159.
108.289.221.159.
159.
)crimeViolent(P
)300thanlessenrollmentandcrimeViolent(P ==
+++
=
6.42 a P(under 20) = .464 + .147 + .237 = .848
b P(retail) = .237 + .035 + .005 = .277
c P(20 to 99 | construction) =
077.
508.
039.
005.039.464.
039.
)onconstructi(P
)onconstructiand99to20(P ==
++
=
6.44 P(purchase | see ad) =
;30.
60.
18.
42.18.
18.
)adsee(P
)adseeandpurchase(P ==
+
=
P(purchase) = .18 +
.12 = .30. The events are independent and thus, the ads are not effective.
6.46 a P(bachelor’s degree | west)
6.47
6.48
6.49
6.50
6.51
6.52
a P(R and R) = .81
6.53 a & b
c 0 right-handers 1
1 right-hander 3
P(1 right-hander) = 3(.009) = .027
6.54a
b P(RR) = .8091
c P(LL) = .0091
6.55a
P(1 right-hander) = 3(90/100)(10/99)(9/98) = .0249
6.56
a P(win both) = .28
b P(lose both) = .30
c P(win only one) = .12 + .30 = .42
6.57
6.58
P(D) = .02 + .018 = .038
6.59
6.60
6.61
6.62
6.63
6.64
6.65
P(does not have to be discarded) = .1848 + .78 = .9648
6.66 Let A = mutual fund outperforms the market in the first year
6.67 Let A = DJIA increase and B = NASDAQ increase
6.68 Define the events: